詹姆斯·琼斯James Hopwood Jeans

詹姆斯·琼斯的父亲是威廉·塔洛克琼斯。William Jeans是一位苏格兰裔议会记者，写了两本关于科学家生平的书。霍普古德这个名字是琼斯母亲的娘家姓；她来自英格兰北部。这是一个非常虔诚的基督教家庭，琼斯是三个孩子中的老大，也是唯一的男孩。琼斯一家在他十八个月大时搬到布莱顿，然后在他三岁时搬到伦敦。

琼斯 在伦敦的商人泰勒学校接受教育，他于1890年入学。他最初感兴趣的科目是古典文学，但很快他的兴趣转向了数学。学校里一位优秀的数学教师鼓励了 琼斯 对这一科目的兴趣，但从小他就表现出对数字的迷恋。关于他童年非凡能力的几个故事表明，他对数字既有兴趣又有好奇心，并且记忆力出众。爱德华·亚瑟·米尔恩 在 [5] 中讲述道：-

他对数字的兴趣很早就产生了，而且根深蒂固：他不仅分解出租车号码，还把遇到的数字记在脑子里……七岁时，他发现了父亲的 logarithm 书，试图弄清它们的用途但失败了，并背下了前二十个左右的七位数 logarithm，直到生命接近尾声时还记得它们。

琼斯 于1896年10月获得数学奖学金后进入剑桥大学三一学院。在那里，他与同年级的 戈弗雷·哈罗德·哈代 是同学。他在剑桥读本科时师从 詹姆斯·惠特布雷德·李·格莱舍、W W Rouse Ball、阿尔弗雷德·诺思·怀特海、R A Herman 和 埃德蒙·泰勒·惠特克。在1898年的数学荣誉学位考试中，他获得 Second 数学荣誉学位考试一等及格者（Wrangler）（在一等学生名单中排名第二），并在1900年的数学荣誉学位考试中获得一等学位。尽管他不会再回到纯数学领域，琼斯 在本科期间写了一篇关于数论的论文。琼斯 和 戈弗雷·哈罗德·哈代 都获得了史密斯奖，'相对功绩未指定'。琼斯 获得了艾萨克 艾萨克·牛顿 天文学和光学学生奖学金，然后在1901年，他被选为三一学院的研究员。

还在本科期间，琼斯就已经在1899-1900学年在卡文迪什实验室工作，获得了实验物理学的经验。他从1901年起非常积极地从事研究，发表了应用数学、物理学和天文学各种主题的著作。特别是他发表了关于气体比热和辐射机制的论文。然而，这些成就是在健康问题的情况下取得的。他在1902年和1903年期间患有肺结核，不得不去疗养院康复。他先在Ringwood、Lyndhurst的疗养院待了一段时间，后来又在Mundesley的疗养院待了一段时间。

在因肺结核被迫休息的这段时间里，琼斯 致力于他的第一部主要著作 The dynamical theory of gases。这是一本包含了许多 琼斯 自己研究的书。爱德华·亚瑟·米尔恩 写道，这部作品包括 [5]：-

……能量均分理论和 詹姆斯·克拉克·麦克斯韦 定律，以及他……处理气体统计力学的章节……以其表达的魅力、阐述的大胆和普遍性的力量使读者倾倒。

爱德华·亚瑟·米尔恩 写道，他在学生时代研究这部作品是他……之一：

……最生动、最令人愉悦的数学体验。

他接着说明这项工作对他产生了怎样的影响，成为他职业生涯的起点：——

这完全是一场愉快的冒险。当我把琼斯的统计力学对一个年轻人思想的冲击，比作初次接触复变函数论时的冲击时，纯粹数学家们会明白我的意思。人们会惊讶地发现，如此丰硕的成果竟源于如此稀薄的假设与定义。

The dynamical theory of gases远不止是对琼斯本人研究的记述。它是对整个领域的学术性论述，包括对气体物理性质的描述。黏性和热传导也是他纳入的其他主题。这本书得益于琼斯在几个方面的专长：他的物理直觉、他的数学技巧，尤其是他以非凡清晰度写作的能力。

1905年，琼斯在Philosophical Magazine上发表了一篇论文，表明以太不可能与物质达到热平衡。当然，马克斯·普朗克在1900年宣布了他的公式，现在称为马克斯·普朗克辐射公式，关于黑体辐射，但琼斯强烈反对马克斯·普朗克的结果，例如见[4]。当然，琼斯的论文可以被视为经典物理学不够用的数学“证明”，但有趣的是，他关于系统达到平衡所需极长时间的前量子观念，以及在分子气体比热测量中观察到的能量均分失效，在琼斯引入它们80多年后的相对近期又被再次使用。我们还应该注意到，琼斯的论文是在Michelson-法兰克·莫雷实验否定了以太的存在之后写的，并且与阿尔伯特·爱因斯坦发表狭义相对论是同一年。

琼斯于1904年被任命为剑桥大学数学讲师，随后从1905年到1909年在普林斯顿讲学，期间担任应用数学教授。在此期间，他出版了他的第二部重要著作Theoretical Mechanics（1906年），然后在1907年，他当选为皇家学会的会士。

1907年，琼斯与美国人Charlotte Tiffany Mitchell结婚，她后来成为一位小有名气的诗人。1908年，他还在美国时出版了The Mathematical Theory of Electricity and Magnetism。1909年，琼斯返回英国，次年他被任命为剑桥大学乔治·加布里埃尔·斯托克斯应用数学讲师。他只担任这个职位直到1912年，然后退休到吉尔福德，全身心投入数学研究和写作。

琼斯继续产出卓越的作品，并于1914年为物理学会撰写了一份关于Radiation and Quantum Theory的优秀报告。在这项工作中，他表明他已经接受了马克斯·普朗克关于黑体辐射的公式，而他在1905年曾拒绝过这个公式。尽管第一次世界大战阻止了琼斯的报告在1918年之前在英国广泛传播，但此后它对量子理论和玻尔原子理论被英国科学界接受产生了重大影响。

1917年，琼斯凭借其题为Problems of cosmogony and stellar dynamics的论文获得了剑桥大学的约翰·柯西·亚当斯奖。该论文于1919年作为书籍出版。然而，繁重的工作量正在造成损害，1917年，琼斯开始出现心脏问题的初步迹象。1918年，琼斯及其家人搬到萨里郡的多金，在那里他们住进了一栋精美的房子克利夫兰小屋。他非常热爱音乐，在家中建造了一架管风琴，他经常每天弹奏三四个小时。尽管才华横溢，他从未公开演奏，甚至没有为朋友演奏过。

琼斯和亚瑟·爱丁顿之间就恒星中能量产生的机制进行了长期的科学争论。琼斯支持能量是收缩结果的理论，但事实证明这是错误的，而亚瑟·爱丁顿当然正确地认为能量来自物质的缓慢湮灭过程。

琼斯在流体方面的工作使他相信皮埃尔·西蒙·拉普拉斯关于太阳系形成的星云假说是错误的。他在其约翰·柯西·亚当斯奖论文中研究了可压缩流体。通过检查旋转流体质量的稳定性，他得出结论：George 乔治·达尔文关于梨形流体稳定的结果是错误的。将计算提高到更高的精度后，他表明该形状实际上是不稳定的。他从这些结果中推导出一种机制，即旋转质量可以分裂成两个，为双星形成提供了模型。

他从自己的结果中推断出[1]：——

……一个聚集质量的旋转显然不可能导致行星系统的形成。

相反，他提出了一种潮汐理论，认为一颗恒星靠近太阳并拉出物质，这些物质凝聚成了行星。他在1922年的爱德蒙·哈雷讲座中解释了他在The nebular hypothesis and modern cosmogony中的理论。1923年，他在加利福尼亚州帕萨迪纳的威尔逊山天文台进行研究，并被任命为研究助理。

琼斯的妻子于1934年去世，他在次年再婚。他的第二任妻子Suzanne Hock来自维也纳，是一位有造诣的音乐家。因此，琼斯在他多金家中又安装了一架管风琴，并运用自己的科学技能设计了家中的声学结构，使他和妻子都能演奏各自的管风琴而互不干扰。

正如我们已经注意到的，琼斯研究热力学、热以及辐射的其他方面，就这些主题及其在天文学中的应用出版了重要著作。除上文提到的以外，他的技术性著作还有Astronomy and Cosmogony（1928）和Introduction to the Kinetic Theory of Gases（1940）。

1928年，琼斯被授予爵士称号。这是他获得的众多荣誉之一；我们将在下面再提到几个。1929年后，琼斯放弃了原创研究，大部分时间用于撰写科普书籍；他一共写了九本这样的书。其中一本这样的书The Universe Around Us（1929年）部分基于他前一年所做的广播讲话。爱德华·亚瑟·米尔恩写道[5]：-

就像他的技术论著一样，这本书从头到尾都保持着读者的兴趣并激发着关注。

他还在1930年做了雷德讲座，该讲座被整理成The Mysterious Universe（1930年）。在这本书中，琼斯写道：-

我们已经不赞成宇宙是由生物学家或工程师规划的可能性；从创造的内在证据来看，宇宙的伟大建筑师现在开始显现为一位纯粹的数学家。

尽管他在天文学和物理学方面有所建树，琼斯始终以数学家的方式思考，并始终认为自己是一位数学家。

其他受欢迎的著作包括The New Background of Science（1933年）、Through Space and Time（1934年）、Science and Music（1938年）和Physics and Philosophy（1943年）。在最后提到的这部著作中，琼斯在序言中解释了这部作品的目的：-

本书的目的很简单：讨论——并在某种程度上探索——物理学与哲学之间的边缘领域，这个领域过去似乎很枯燥，但通过理论物理学的近期发展，突然变得如此有趣和重要。这种新的兴趣远远超出了物理学和哲学的技术问题，延伸到与人类生活密切相关的问题，如唯物主义和自由意志。因此，我希望这本书能引起那些既不是职业物理学家也不是职业哲学家的人的兴趣。

这部著作考察了琼斯所称的从艾萨克·牛顿到阿尔伯特·爱因斯坦的“机械时代”，马克斯·普朗克、卢瑟福和尼尔斯·玻尔的“新物理学”，以及与玻尔、维尔纳·海森堡、路易·德布罗意、埃尔温·薛定谔和保罗·狄拉克一起的“从表象到实在”。尽管琼斯从未发表过对量子理论的原创性贡献，但他在这些通俗著作中表明他紧跟这一领域的发展。[2]：-

……[琼斯通俗著作]的惊人销量只有少数富有想象力或宗教性的作品能与之匹敌。让的文学成功本可以从他的论文中预测到，其中非数学部分即使外行也能欣赏。作为科学阐述，这些通俗著作是无与伦比的。

琼斯在1945年1月心脏病发作，但恢复良好，并于1946年7月与妻子去蒙特勒度假。然而，在9月第二次心脏病发作后，琼斯在家中去世。爱德华·亚瑟·米尔恩在[5]中记载，琼斯最后一天的部分时间是在听音乐中度过的。

琼斯获得的荣誉太多，无法在此完整记录。让我们记下几项，例如：获皇家天文学会金质奖章（1922），当选皇家天文学会主席（1925—27），获富兰克林奖章（1931），当选英国协会 for the Advancement of Science主席（1934），获Mukerjee奖章（1937），获加尔各答奖章（1938），获功绩勋章（1939），当选皇家学会副主席（1938—40）。授予他荣誉博士学位的大学包括牛津、曼彻斯特、贝拿勒斯、阿伯丁、约翰威廉·霍普金斯、圣安德鲁斯、都柏林和加尔各答。

让我们以进一步引用The Mysterious Universe（1930年）中的内容来结束：-

世俗的纯数学家不关心物质实体，只关心纯粹思想。他的创造不仅由思想创造，而且是纯粹思想。……而那些现在似乎对我们理解自然至关重要的概念……四维空间，一个永远膨胀的空间；一系列遵循概率定律而非因果律的事件；所有这些概念在我看来都是纯粹思想的构造。在我看来，自然所遵循的定律，与其说像机器在运动中遵循的定律，不如说像音乐家在写赋格曲或诗人在创作十四行诗时所遵循的定律。……如果这一切都是如此，那么宇宙最好被描绘成——尽管仍然非常不完美和不充分——由纯粹思想构成，这种思想，由于缺乏更宽泛的词，我们必须描述为数学思想者的思想。

James Jeans' father was William Tullock Jeans. William Jeans was a parliamentary journalist of Scottish descent who wrote two books on the lives of scientists. The name Hopgood was James mother's maiden name; she came from the north of England. It was a very religious Christian family with James the eldest of the three children and the only boy. James' family moved to Brighton when he was eighteen months old then, when he was three years old, they moved to London.

Jeans was educated in Merchant Taylor's School in London which he entered in 1890. The first topic which interested him was classics but soon his interests turned towards mathematics. An excellent mathematics teacher at the school encouraged Jeans' interest in the subject but from the time he was a young child he had shown a fascination with numbers. Several stories about his remarkable abilities as a child indicate both an interest and curiosity about numbers and an outstanding memory. Milne relates in [5] that:-

His interest in numbers was early and deep-seated: he not only factorised cab-numbers, but retained in his memory the numbers that he encountered ... At the age of seven he found his father's book of logarithms, tried to discover what they were for but failed, and learnt the first twenty or so seven-figure logs by heart, and remembered them until near the end of his life.

Jeans went to Trinity College Cambridge in October 1896 having won a mathematical scholarship. There he was a fellow student with G H Hardy who was in the same year. He was taught as an undergraduate at Cambridge by J W L Glaisher, W W Rouse Ball, A N Whitehead, R A Herman and E T Whittaker. He was Second Wrangler in the Mathematical Tripos examinations of 1898 (ranked seconf in the list of First Class students) and was awarded a First Class degree in the Mathematical Tripos of 1900. Although he would not return again to pure mathematics, Jeans wrote a paper on the theory of numbers while an undergraduate. Both Jeans and Hardy were awarded a Smith's prize with 'unspecified relative merit'. Jeans was awarded an Isaac Newton Studentship in astronomy and optics, then in 1901 he was elected a Fellow of Trinity.

Already while he was still an undergraduate Jeans had gained experience in experimental physics having worked in the Cavendish Laboratory during the academic year 1899-1900. He was very active in research publishing work on a variety of topics in applied mathematics, physics and astronomy from 1901 onwards. In particular he published on the specific heats of gases and the mechanism of radiation. However this was achieved despite health problems. He suffered from tuberculosis during 1902 and 1903 and he had to go to a sanatorium to recover. He spent some time at a sanatorium in Ringwood, Lyndhurst, then later at a sanatorium in Mundesley.

During this period of forced rest due to the tuberculosis, Jeans worked on his first major text The dynamical theory of gases. It was a book which incorporated much of Jeans own researches. Milne writes that the work includes [5]:-

... the theory of the equipartition of energy and Maxwell's law, and the chapters in which he ... treats the statistical mechanics of a gas ... sweep the reader off his feet by their charm of expression, boldness of exposition, and power of generality.

Milne writes that studying this work when he was a student was one of his:-

... most vivid and pleasurable mathematical experiences.

He goes on to show what an impact the work had on him as the start of his career:-

It is all a joyous adventure. Pure mathematicians will know what I mean when I describe the effect of the impact of Jeans' statistical mechanics on a young man's mind as comparable with the impact of a first introduction to the theory of functions of a complex variable. One is astounded that such a rich harvest of results arises from so thin a sowing of assumptions and definitions.

The dynamical theory of gases is far more than an account of Jeans' own research. It is a scholarly account of the whole area including a description of the physical properties of gases. Viscosity and conduction of heat are other topics which he included. The book benefits from Jeans' expertise in several areas: his physical intuition, his mathematical skills, and not least his ability to write with extraordinary clarity.

In 1905 Jeans published a paper in the Philosophical Magazine which showed the impossibility of the ether reaching thermal equilibrium with matter. Of course Planck had announced in 1900 his formula, now known as Planck's radiation formula, on black-body radiation but Jeans was strongly opposed to Planck's results, see for example [4]. Of course Jeans' paper can be seen as a mathematical "proof" that classical physics does not suffice, but it is interesting to note that his pre-quantum ideas concerning the very long time required for systems to come into equilibrium and the observed breakdown of equipartition in specific heat measurements on molecular gases have been used again in relatively recent times more than 80 years after Jeans introduced them. We should also note that Jeans' paper was written after the Michelson-Morley experiment disproved the existence of the ether, and in the same year that Einstein published the special theory of relativity.

Jeans was appointed a Lecturer in Mathematics at Cambridge in 1904, then he lectured at Princeton from 1905 until 1909 where he was Professor of Applied Mathematics. During this period he published his second major text Theoretical Mechanics (1906) and then, in 1907, he was elected a Fellow of the Royal Society.

In 1907 Jeans married an American, Charlotte Tiffany Mitchell, who became a poet of some note. He published The Mathematical Theory of Electricity and Magnetism in 1908 while still in the United States. In 1909 Jeans returned to England and the following year he was appointed Stokes Lecturer in Applied Mathematics at Cambridge. He only held this post until 1912 when he retired to Guildford to devote himself completely to mathematical research and writing books.

Certainly Jeans continued to produce a remarkable output, and he wrote an excellent report on Radiation and Quantum Theory for the Physical Society in 1914. In this work he showed that he had come to accept Planck's formula on black-body radiation which he had rejected in 1905. Although World War I prevented Jeans' report from being widely read in Britain until after 1918, it then had a major impact on having quantum theory and the Bohr theory of the atom accepted by the British scientific community.

In 1917 Jeans won the Adams Prize from the University of Cambridge for his essay entitled Problems of cosmogony and stellar dynamics. This was published as a book in 1919. The high work-load was taking its toll, however, and in 1917 Jeans began to show his first signs of heart problems. In 1918 Jeans and his family moved to Dorking, Surrey, where they occupied a fine house Cleveland Lodge. He was a great lover of music and in his home he had an organ built which he often played for three or four hours a day. Despite considerable talents, he never played in public, not even playing for his friends.

There was a long running scientific argument between Jeans and Eddington over the mechanism by which energy was created in stars. Jeans favoured, incorrectly as it turned out, the theory that the energy was the result of contraction while Eddington, correctly of course, believed it resulted from a slow process of annihilation of matter.

Jeans' work in fluids led him to believe that Laplace's nebular hypothesis for the creation of the solar system was incorrect. He had studied compressible fluids in his Adams Prize essay. Examining the stability of a rotating mass of fluid he concluded that the result of George Darwin which showed that a pear shape of fluid was stable, was wrong. Taking the calculations to a higher degree of accuracy he showed that the shape was in fact unstable. He deduced from these results a mechanism whereby the rotating mass can split into two, giving a model for double star formation.

From his results he deduced that [1]:-

... rotation of a concentrating mass evidently could not give rise to the formation of a planetary system.

Instead he proposed a tidal theory based on a star passing close to the Sun and pulling matter out which condensed into the planets. He explained his theories in The nebular hypothesis and modern cosmogony in his Halley lecture of 1922. In 1923 he undertook research at the Mount Wilson Observatory in Pasadena, California where he was appointed as Research Associate.

Jeans' wife died in 1934 and he remarried in the following year. His second wife, Suzanne Hock, came from Vienna and she was an accomplished musician. Jeans, therefore, had a second organ installed in his Dorking home and, using his scientific skills, he designed the acoustics in his house to allow both his wife and himself to play their organs without disturbing each other.

As we have noted Jeans worked on thermodynamics, heat and other aspects of radiation, publishing major works on these topics and on applications to astronomy. His technical books, other than those mentioned above, are Astronomy and Cosmogony (1928), and Introduction to the Kinetic Theory of Gases (1940).

In 1928 Jeans was knighted. This was one of a great number of honours which he received; we shall note a few more below. After 1929 Jeans gave up original research and spent most of his time writing popular texts; he wrote nine such texts in all. One such book The Universe Around Us (1929) was based in part on broadcast talks he had given in the previous year. Milne writes [5]:-

Like his technical treatises, this book sustains the reader's interest and excited attention from cover to cover.

He also gave the Rede lecture in 1930 which was written up as The Mysterious Universe (1930). In this Jeans writes:-

We have already considered with disfavour the possibility of the universe having been planned by a biologist or an engineer; from the intrinsic evidence of the creation, the Great Architect of the Universe now begins to appear as a pure mathematician.

Really despite his work in astronomy and physics, Jeans always thought as a mathematician and always considered himself a mathematician.

Further popular texts included The New Background of Science (1933), Through Space and Time (1934), Science and Music (1938), and Physics and Philosophy (1943). In this last mentioned text Jeans explains in the preface the purpose of the work:-

The aim of the present book is very simply stated; it is to discuss - and to some extent to explore - that borderland territory between physics and philosophy which used to seem so dull, but suddenly became so interesting and important through recent developments of theoretical physics. The new interest extends far beyond the technical problems of physics and philosophy to questions which touch human life very closely, such as materialism and free-will. Thus I hope the book may interest many who are neither physicists nor philosophers by profession.

The work examines what Jeans calls the 'mechanical age' from Newton to Einstein the 'new physics' of Planck, Rutherford, and Niels Bohr and 'From appearance to reality' with Bohr, Heisenberg, de Broglie, Schrödinger, and Dirac. Although Jeans never published original contributions to quantum theory, he showed in such popular books that he had kept up with the developments in this area. The [2]:-

... phenomenal sales [of Jeans popular books] were equalled only by a few imaginative or religious works. Jean's literary success might have been predicted from his treatises, where the non-mathematical sections can be enjoyed even by the layman. As expositions of science these popular books are unexcelled.

Jeans had a heart attack in January 1945 but made a good recovery and, in July 1946 went on holiday with his wife to Montreux. However after a second heart attack in September Jeans died in his home. Milne records in [5] that Jeans spent part of his last day listening to music.

The honours which Jeans received are far too numerous to give a full record here. Let us note a few such as: awarded the Gold Medal of the Royal Astronomical Society (1922), elected President of the Royal Astronomical Society (1925-27), awarded the Franklin Medal (1931), elected President of the British Association for the Advancement of Science (1934), awarded the Mukerjee Medal (1937), awarded the Calcutta Medal (1938), received the Order of Merit (1939), elected vice-President of the Royal Society (1938-40). Among the universities to give him an honorary doctorate were Oxford, Manchester, Benares, Aberdeen, Johns Hopkins, St Andrews, Dublin, and Calcutta.

Let us end by quoting further from The Mysterious Universe (1930):-

The terrestrial pure mathematician does not concern himself with material substance but with pure thought. His creations are not only created by thought but are pure thought. ... And the concepts which now seem to be fundamental to our understanding of nature ... four dimensional space, a space which expands forever; a sequence of events which follows the laws of probability instead of the laws of causation; all these concepts seem to my mind to be structures of pure thought. To my mind the laws which nature obeys are less suggestive of those which a machine obeys in its motion than those which a musician obeys in writing a fugue, or a poet in composing a sonnet. ... If all this is so, then the universe can best be pictured, although still very imperfectly and inadequately, as consisting of pure thought, the thought of what, for want of a wider word, we must describe as a mathematical thinker.